In the literature, some universal relations between the BE and \(C\)  have been proposed, such as that[1]} based on the radius of a \(1.4 M_\odot \)  NS, \(R_{1.4}\) , \(M^{*}=M+R_{1.4}^{-1} \times M^{2}\) , with \(1.8 \%\)  relative error. Note that the \(1.4 M_\odot \)  selection is close to the most probable for primary companions in DNSs. In order to illustrate our findings we consider two EoS i.e. DD2 and SFHo [2]}, whose M(R) relationship is shown in Fig.(1) left panel. For SFHo it is found a saturation density \(n_0=0.1583\)  \(\rm fm^{-3}\) , nuclear incompressibility \(K=245.4\)  MeV, symmetry energy \(J=31.57\)  MeV and a logarithmic derivative of the symmetry energy \(L=47.10\)  MeV. For the DD2 \(n_{0}=0.1491\mathrm {fm}^{-3}\) , \(K=242.7\)  MeV, \(J=31.78\)  MeV and \(L=55.19\)  MeV. Using existing data[3]} from BNS simulations we obtain \(R^{\rm DD2}_{1.4}=13.5 \pm 0.1\)  km, \(R^{\rm SFHo}_{1.4}= 11.8 \pm 0.1\)  km, see Fig.(1) right panel. Considering the sum of BE of both NSs described by a given EoS, \(BE_1+BE_2\) , we arrive at values for DD2: \(BE_1+BE_2=0.25\pm 0.04M_{\odot }\)  and SFHo: \(BE_1+BE_2=0.28\pm 0.04M_{\odot }\)  which fulfill the fitted form[4]} \(\frac{BE_i}{M_i}=-0.0130+0.618 C_i+0.267 {C^2_i}\)  where \(C_i=\frac{G M_i}{R_i c^2}\)  is the compactness. They retain the \(M(R)\)  relationship from \(C\)  and \(M\)  values.
